In a large saucepan, heat the olive oil over medium heat. Add the chopped onions and sauté until softened, for about 3-4 minutes. Add the diced carrot and sliced leeks, and stir regularly until all ingredients have softened and lightly caramelized. You can sprinkle a little salt into the saucepan to speed things up.
Add the minced or grated garlic and once fragrant, stir in the dried thyme. Toss everything to coat the veggies in the herb and after heating through for a minute, pour in the vegetable stock.
Bring everything to a simmer, then add a lid to the saucepan and reduce the heat. Let everything simmer for 5-8 minutes for the flavors to meld together.
Add in the drained cannellini beans, and once heated through, use a stick blender to blend roughly ¼ of the soup to give it a creamy texture. Stir well, and simmer on low heat for 10 minutes, then season to taste with salt and pepper.
To serve, garnish the soup with fresh thyme and enjoy alongside a slice of freshly toasted bread.